Calculus

posted by .

The area bounded by the curve y = 2x^2-x^3 and line y=0 is rotated around the y-axis. The volume of the resulting structure can be expressed as V = a(pi)/b, where a and b are coprime positive integers. What is the value of a + b?

  • Calculus -

    Using shells:
    v = ∫[0,2] 2πrh dx
    where r = x and h = y = 2x^2 - x^3
    v = 2π∫[0,2] 2x^3 - x^4 dx
    piece of cake from here on

  • Calculus -

    16/5=21

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Determine the volume of the solid abtained when the region bounded by y=sqrt x and the line Y=2 and x=0 is rotated: (i) about the x-axis (ii) about the line x=4. (i) Each element of the body of revolution with thickness dx, has area …
  2. Calculus

    Let R be the region bounded by the x-axis, x = 5 and the curve y = x. This region is rotated around the x-axis. Find the volume of the resulting solid. (Note: R is a triangular region. The resulting solid has a simple shape. You may …
  3. calculus

    The region bounded by the curve y=1รท(1+2x) , the line X=2 , the x-axis and the y axis is rotated completely about the y-axis. Show that the volume generated is 1/2π(4-ln5)
  4. Math

    Find the volume generated when the area bounded by the curve y^2 = 16x, from x = 0 to x = 4 is rotated around the x-axis.
  5. calculus

    The region A is bounded by the curve y=x^2-5x+6 and the line y = -x + 3. (a) Sketch the line and the curve on the same set of axes. (b) Find the area of A. (c) The part of A above the x-axis is rotated through 360degree about the x-axis. …
  6. Calculus

    1. Find the area of the region bounded by the curves and lines y=e^x sin e^x, x=0, y=0, and the curve's first positive intersection with the x-axis. 2. The area under the curve of y=1/x from x=a to x=5 is approximately 0.916 where …
  7. calculus

    The area bounded by the curve 2y^2=x and the line 4y=x is rotated around the y-axis. The volume of the resulting structure can be expressed as V=a/bπ, where a and b are coprime positive integers. What is the value of a+b?
  8. calculus

    The area bounded by the curve 2y^2=x and the line 4y=x is rotated around the y-axis. The volume of the resulting structure can be expressed as V=a/bπ, where a and b are coprime positive integers. What is the value of a+b?
  9. calculus 1

    Set up the simplified integral and compute the volume created when the area bounded by y=.25x4, y=4, and the y=axis (Quadrant 1) is rotated around the line x=-2
  10. Calculus

    Volume created when the area bounded by the curve y = 1/x, the x-axis, and the lines x = 1 and x = 4 is rotated about: a) the x-axis: 2.356 units^3 Is this correct?

More Similar Questions